HALF-SPACE ANALYSIS OF THE DEFECT-CORRECTION METHOD FOR FROMM DISCRETIZATION OF CONVECTION.

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Bibliographic Details
Title:	HALF-SPACE ANALYSIS OF THE DEFECT-CORRECTION METHOD FOR FROMM DISCRETIZATION OF CONVECTION.
Authors:	Diskin, Boris¹ bdiskin@icase.edu, Thomas, James I.¹ j.l.thomas@larc.nasa.gov
Source:	SIAM Journal on Scientific Computing. 2000, Vol. 22 Issue 2, p633-655. 23p.
Subjects:	Defect correction methods (Numerical analysis), Numerical analysis, Approximation theory, Iterative methods (Mathematics), Stochastic convergence, Mathematical functions, Asymptotic expansions
Abstract:	A novel, comprehensive, discrete, half-space analysis for the defect-correction method has been developed. This analysis plays the same role for nonelliptic-problem solvers as the full-space Fourier mode analysis plays for elliptic-problem solvers. Numerical simulations confirm the accuracy of the half-space analysis. The following important findings about the defect-correction method applied to the Fromm discretization of the two-dimensional convection equation are reported: 1. The initial convergence rate of the defect-correction method is principally a function of the relative accuracy of the operators involved in the defect-correction iterations. 2. The asymptotic convergence rate is about 0.5 per defect-correction iteration. 3. If the driver operator is first-order accurate, then the initial convergence rates may be slow. The number of iterations required to get into the asymptotic convergence regime or/and to converge the algebraic error below the discretization-error level can be proportional to h- 1/3. This h-dependent delay is a multidimensional phenomenon—it cannot be observed in one-dimensional problems, and it disappears in the case of close alignment between the grid and the convection equation characteristic. 4. If the driver operator is second-order accurate, the defect-correction solver demonstrates the asymptotic convergence rate from the very beginning. Only one defect-correction iteration is required to converge algebraic error substantially below the discretization-error level. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	A novel, comprehensive, discrete, half-space analysis for the defect-correction method has been developed. This analysis plays the same role for nonelliptic-problem solvers as the full-space Fourier mode analysis plays for elliptic-problem solvers. Numerical simulations confirm the accuracy of the half-space analysis. The following important findings about the defect-correction method applied to the Fromm discretization of the two-dimensional convection equation are reported: 1. The initial convergence rate of the defect-correction method is principally a function of the relative accuracy of the operators involved in the defect-correction iterations. 2. The asymptotic convergence rate is about 0.5 per defect-correction iteration. 3. If the driver operator is first-order accurate, then the initial convergence rates may be slow. The number of iterations required to get into the asymptotic convergence regime or/and to converge the algebraic error below the discretization-error level can be proportional to h- 1/3. This h-dependent delay is a multidimensional phenomenon—it cannot be observed in one-dimensional problems, and it disappears in the case of close alignment between the grid and the convection equation characteristic. 4. If the driver operator is second-order accurate, the defect-correction solver demonstrates the asymptotic convergence rate from the very beginning. Only one defect-correction iteration is required to converge algebraic error substantially below the discretization-error level. [ABSTRACT FROM AUTHOR]
ISSN:	10648275
DOI:	10.1137/S1064827599358637